Tensor Products, Polynomials
and Holomorphic Functions on Banach Spaces
There is a research
team working in this area, consisting of Dr
RAY RYAN, a Senior Lecturer in the department, Dr BOGDAN GRECU, a
Postdoctoral Fellow and JOHN LOANE, a
PhD student. In broad terms, we are
interested in multiple tensor products of Banach spaces, ideals
of multilinear forms, homogeneous polynomials and holomorphic functions
on Banach spaces. The team is funded
by a Basic Research Grant from Enterprise Ireland.
RAY RYAN is a Senior Lecturer in Mathematics. He
is particularly interested in tensor products and operator ideals on Banach
spaces and their connections with homogeneous polynomials and holomorphic
functions. He is the author of the
book "Introduction
to Tensor Products of Banach Spaces" (Springer
Monographs in Mathematics, 2001). His
previous PhD students are Padraig Kirwan (PhD 1997, "Complexification of
Multilinear and Polynomial Mappings on Normed Spaces") and Bogdan Brecu
(PHD 2001, "Geometrical Properties of Spaces of Homogeneous Polynomials").
He
is currently working on monomial expansions for homogeneous polynomials
and holomorphic functions on Banach spaces with unconditional Schauder
bases, and on Banach lattice structures in spaces of homogeneous polynomials.
BOGDAN GRECU is a Postdoctoral Fellow. His
PhD thesis was a study of the extreme points and smooth points on the unit
ball of the space of n-homogeneous polynomials, particularly on real and
complex Hilbert spaces. He is currently
working on symmetric and alternating
tensor products of stable Banach spaces and on tensor product bases
in symmetric tensor products of Banach spaces with unconditional Schauder
bases.
JOHN LOANE is a PhD student. His first degree was a B.A.(mod) in Mathematics
from Trinity College Dublin, followed by an M.Sc. in High Performance Computing,
also from Trinity College. He is currently
working on polarization inequalities for homogeneous polynomials.
RECENT PREPRINTS
Bogdan
C. Grecu and Raymond A. Ryan,
"Schauder Bases for Symmetric Tensor Products" [PDF] [PS]
"Tensor Products of Direct Sums" [PDF] [PS]
